Why is the node editor showing different kinds of nodes?
This answer is was for older versions (2.79 and previous)
For blender version 2.8x read this

Without any addons, the Node Editor can be used in three different modes:

You are looking at the cycles material (shader) nodes. The tutorial is using the compositor nodes.
Simply click on the Compositing button in the Node Editor header to switch to the compositor nodes.

Also make sure the Use nodes box is checked.